SQL & PL/SQL :: User-defined Aggregate Calculation For Z Score

I'm calculating a Z score based on some simple numerical data thus:

create table t (id number, val number);

insert into t values(1, 1795);
insert into t values(2, 1753);
insert into t values(3, 1743);
insert into t values(4, 1876);
insert into t values(5, 1848);

[Code] .....

the logic is quite simple - calculate a moving average over the previous 12 rows, and a stdev over the same window. Then subtract the prior row's moving average from the current value, and divide by the prior row's stdev.

The issue is I want to expose this logic in a BI tool (OBI EE v10g), meaning I can't use the nested analytic functions. How to achieve this logic in a single analytic pass? The sql above took about 2 minutes to write this morning, then I've spent all day looking at user-defined aggregate functions, but haven't even been able to get the first step, the moving average, working. I can understand that I can probably create an udaf to replicate the avg(val) over (order by id ROWS BETWEEN 11 PRECEDING AND 0 FOLLOWING) functionality, but I can't see how to bundle the logic for the other three steps in the calculation into this.

From what I've read, the ODCIAggregateMerge should allow me to combine different threads that can return the different values I need for the current row calculation. Is this correct?

The only example udafs I can find are either not relevant (STRAGG) or very simple (ie don't appear to invoke multiple passes). I've also had a look at the COLLECT function, but again I can't see a way to use this.